Space radar imaging is different from optical imaging, which is well known, and which relies on physical principles close to those of human vision. The image acquired by a space radar differs firstly in that its contents differs from that obtained by means of a conventional optical system since the scene is observed by the space radar at a decimeter wavelength (3 cm to 25 cm) which is much greater than the micrometer wavelength used in traditional optics. The image also differs in the way in which it is acquired, since a space radar is an active instrument which includes its own source for illuminating the scene, thereby making observation possible by night as well as by day, and by an appropriate choice of wavelength, making observation insensitive to cloud. It therefore provides "all-weather" imaging which gives numerous operational advantages. However, since it is difficult to deploy antennas that are more than 10 meters long in space, the natural angular resolution of space radars is very poor, being of the order of half a degree (whereas the human eye is about ten times better). Radar imaging therefore does not rely on the natural resolution of the instrument. Resolution in the direction perpendicular to the flight direction is obtained by analysis on board the satellite of echo return times (the principle on which all radars are based), and in the direction parallel to the flight direction, by a digital process known as "aperture synthesis", which process is performed on the ground and requires large amounts of computation. Each of the lines of a radar "image" corresponds to a pulse emitted by the radar and transformed into a run of samples ordered by their return times giving column indices for the image. The samples are complex numbers representative of the amplitude and of the phase of the reflected wave. The above-mentioned digital process of aperture synthesis conserves the complex nature of the signals processed, such that, in addition to its main operational quality, i.e., that of being insensitive to cloud and being capable of operating at night, a space radar installed on a satellite makes it possible to measure small displacements by means of the technique of interferometry.
The phase of the reflected wave contains information concerning the position, the distribution, and the radioelectric nature of elements constituting the scene illuminated by the radar, also known as "targets" (such as pebbles, branches, etc.). By comparing radar images taken at different dates and under almost identical conditions, position information can be isolated from other information by constructing an interferogram. Radar interferometry was proposed and tested more than 20 years ago, and reference may usefully be made to the article published by L. C. Graham in IEEE Proceedings, Vol. 62, No. 6, Jun. 1974, entitled "Synthetic interferometer radar for topographic mapping".
Phase information is influenced by three factors, of which the first two are unknown:
the phase shift caused by reflection of the radar wave on targets, and associated with the electromagnetic properties of the targets; PA1 the phase shift associated with the relative positions of the targets within a common image element or "pixel". The resultant phase of a pixel is the result of a complex combination of the contributions from the various targets present within the pixel, and weighted by their respective amplitudes; and PA1 the phase shift that may possibly be due to targets moving or to a change of observation conditions. PA1 the trajectories of the satellite becoming orbitally closer or more distant between acquiring images. As mentioned above, the orbits must be close but they are never identical, nor even parallel in practice; PA1 a stereoscopic effect produced by the topography when observed from two viewpoints that are slightly different; PA1 overall movement of the target as a whole that has taken place between acquiring the images; and PA1 variations in atmospheric propagation length and variations in phase due to the ionosphere. These are also known as "non-Euclidean" effects since the phase variations to which various wavelengths are subjected cannot be explained by a common increase or decrease in optical path length. PA1 an effect due to the ground moving must appear on all interferograms covering a given time interval, whatever the orbital differences between pictures being taken. For example, if the ground appears to have moved in an interferogram constructed from images acquired in April and in May, then it must also be present in an interferogram constructed from images acquired in March and in June; and PA1 an effect due to atmospheric propagation must be found in all of the interferograms containing contributions from any particular image that has been effected by this propagation effect. PA1 forming first and second interferograms from pairs of radar images obtained by using two respective space radars operating at respective wavelengths .lambda..sub.1 and .lambda..sub.2 satisfying the relationship m.lambda..sub.1 =n.lambda..sub.2 where m and n are integers, these radars being placed on the same satellite; and PA1 performing the linear combination n.phi..sub.1 -m.phi..sub.2 of respective phases .phi..sub.1 and .phi..sub.2 of the first and second interferograms, with the fractional portion of these linear combination being representative of the non-Euclidean effects affecting the images of these space radars used in making the interferograms. Most preferably, m=2 or m=3, and n=1.
When implementing radar interferometry techniques, it is assumed that the first two factors, although unknown, are stable over time. For the first factor, this assumption implies that the targets are physically stable, and for the second factor, it implies geometrical stability restraining possible variation in the angle of incidence of the radar between two passes of the satellite. Thus, the surface state of the ground must not change excessively between acquiring two images (which rules out the surface of the sea, for example), and the satellite must follows its earlier trajectory very closely (to within a few hundreds of meters at most).
If the above assumption is true, then changes of phase due to the third factor between two radar images can be obtained by constructing an interferogram which represents differences in phase between the two images. These differences can be considered as being the result of four contributions:
In practice, it is difficult to evaluate separately the contribution of each of the factors that has an influence on phase.
Nevertheless, the following considerations can be of some help:
Non-Euclidean effects can be evaluated by deduction after quantifying the other factors that affect phase. This quantification is nevertheless made difficult by the fact that distance measurement is ambiguous, since it is only given modulo the wavelength .lambda. of the radar. In other words, if the wavelength is 5 cm, a 2 cm displacement looks the same as a 7 cm displacement. Complete measurement can be built up by "unwrapping" phase over the image from one point to another so as to show up integer numbers of wavelengths missing from the measurement. Reference may usefully be made to the article entitled "Satellite radar interferometry: two-dimensional phase unwrapping" by Goldstein et al., published in Radio Science, Vol. 23, No. 4, pp. 713 to 720, July-August 1988. Nevertheless, the phase unwrapping operation is difficult to automate and, to the knowledge of the Applicant, there exists no method that makes it possible to evaluate non-Euclidean effects easily and accurately.